You're correct that the text of FARs does not explicitly require a prior personal relationship. However, as they are applied and interpreted in practice, you're almost guaranteed to get in hot water if you fly-share as a private pilot on a regular basis with people you don't know. And that's really not news to anyone with a private pilot certificate or anyone who has spent time looking into getting one.
Agreed, there is no 14 CFR (part 61 or other) regulation that I'm aware of. But the regulations are very concise, and not thorough enough to evaluate every possible scenario.
The point of the FAA's letters is to address the many variations and nuances with real world application of the regulations. And they do so in very readable language (in contrast to regulations). I've found them to be the best guidance on the FAA's opinions & likely actions when the regulations are vague and/or unclear.
I personally use prior personal relationship as a strong guide. One personal exception: I believe I'd be ok sharing costs on a flight with members of my flying club (all pilots or student pilots) who I do not currently know, so long as the means of establishing the flight is more private (club newsletter) than public.